The noncancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group
Abstract
The groups we consider in this study belong to the class Xo of all finitely generated groups with finite commutator subgroups. We shall eventually narrow down to the groups of the form T)<lw zn for some nE N and some finite abelian group T. For a Xogroup H, we study the noncancellation set, X(H), which is defined to be the set of all isomorphism classes of groups K such that H x Z ~ K x Z. For Xogroups H, on X(H) there is an abelian group structure [38], defined in terms of embeddings of K into H, for groups K of which the isomorphism classes belong to X(H). If H is a nilpotent Xogroup, then the group X(H) is the same as the HiltonMislin (see [10]) genus group Q(H) of H. A number of calculations of such HiltonMislin genus groups can be found in the literature, and in particular there is a very nice calculation in article [11] of Hilton and Scevenels. The main aim of this thesis is to compute noncancellation (or genus) groups of special types of .Xogroups such
as mentioned above. The groups in question can in fact be considered to be direct products of metacyclic groups, very much as in [11]. We shall make extensive use of the methods developed in [30] and employ computer algebra packages to compute determinants of endomorphisms of finite groups.
Related items
Showing items related by title, author, creator and subject.

The noncancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group
Mkiva, Soga Loyiso Tiyo (University of the Western Cape, 2008)The groups we consider in this study belong to the class X0 of all nitely generated groups with nite commutator subgroups. We shall eventually narrow down to the groups of the form T owZn for some n 2 N and some nite ... 
Conjugacy classes of some projective linear groups
Dietrich, Ernest Arthur (University of the Western Cape, 1992)Given a finite set X of distinct symbols the symmetric group Sx and the alternating group Ax are obtained without further constructions. More interesting groups are contrived, however, by imposing a certain structure on ... 
Computing Mislin genera of certain groups with nonabelian torsion radicals
Hess, Victor George (University of the Western Cape, 2004)In this minithesis we present some generalities of noncancellation and localization and we compute noncancellation groups. We consider groups belonging to the class X0 of all finitely generated groups that have finite ...